Finite Group Databasebeta

← C2×#10591663 #11861063

Subgroups — C2×#10591663 #11861063

Order 1152.

1061 conjugacy classes of subgroups.

The subgroup lattice has 617 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64159C211yesmaximal, characteristic
2C2×C3×#948C211yesmaximal, characteristic, complemented
3C2×#63817C211yesmaximal, characteristic, complemented
4C2×C3×#837C211yesmaximal, characteristic, complemented
5#10591663C218yesmaximal, direct product factor
6C2×#63578C211yesmaximal, characteristic, complemented
7C2×#63570C211yesmaximal, characteristic, complemented
8C2×#63554C211yesmaximal, characteristic, complemented
9C2×#5145—31nomaximal
10C2×#4823—31nomaximal
11C2×C32×#41C2211yescharacteristic
12C2×#3828C2211yescharacteristic
13#64159C414yescomplemented
14#64159C2214yes—
15C2×#3756C411yescharacteristic, complemented
16C2×#3755C411yescharacteristic, complemented
17C2×#3754C411yescharacteristic, complemented
18C2×#3753C411yescharacteristic, complemented
19C22×C3⋊(C3⋊C8)C2211yescharacteristic
20C3×#948—22no—
21C3×#948C2214yescomplemented
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×#208—21no—
24C2×C3×#208C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C22×C3×C3⋊C8—21no—
27C22×C3×C3⋊C8C2211yescharacteristic
28C2×#3712—21no—
29#63817—22no—
30#63817C2214yescomplemented
31C2×#3710—21no—
32C3×#837C2214yescomplemented
33#63578C2214yescomplemented
34#63570C2214yescomplemented
35#63554C2214yescomplemented
36C2×C3×#131—31no—
37C2×#950—31no—
38C2×#950—31no—
39C2×#950—61no—
40C2×#948D311yescharacteristic, complemented
41C2×#907—31no—
42C2×#901—31no—
43C2×C3×#104—31no—
44C2×#837D311yescharacteristic, complemented
45#5145—38no—
46C2×#825—31no—
47C2×#822—31no—
48C2×#822—31no—
49C2×#815—31no—
50C2×#805—31no—
51C2×#803—31no—
52#4823—38no—
53C32×#41—21no—
54C32×#41—21no—
55C32×#41C2×C412yes—
56C32×#41C2312yes—
57C2×C32×Q8C2×C411yescharacteristic
58C2×C32×D4—21no—
59C2×C32×D4C2×C411yescharacteristic
60C22×C32×C4—21no—
61C22×C32×C4C2311yescharacteristic
62C2×#638—21no—
63#3828—21no—
64#3828—21no—
65#3828C2×C412yes—
66#3828C2312yes—
67C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×#634C2×C411yescharacteristic
70C22×C3×Dic3—21no—
71#3756C2×C414yescomplemented
72#3755C2×C414yescomplemented
73#3754C2×C414yescomplemented
74#3753C2×C414yescomplemented
75C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
76C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
77C2×C3⋊(C3⋊C8)C2×C412yes—
78C2×C3⋊(C3⋊C8)C2312yes—
79C3×C4×Dic3—21no—
80C3×C4×Dic3C2312yes—
81C3×#208—21no—
82C3×#208—21no—
83C3×#208—24no—
84C3×#208C2312yes—
85C3×#208C2312yes—
86C2×C3×C3⋊C8—21no—
87C2×C3×C3⋊C8—21no—
88C2×C3×C3⋊C8—24no—
89C2×C3×C3⋊C8D411yescharacteristic
90C2×C3×C3⋊C8D411yescharacteristic
91C2×C3×C3⋊C8D412yes—
92C2×C3×C3⋊C8C2312yes—
93#3712—24no—
94#3710—24no—
95C2×#444—91noSylow
96C2×C3×#41—21no—
97C2×C3×#41C2×D311yescharacteristic
98C2×C3×#41C2×D311yescharacteristic
99C2×#235—31no—
100C2×#235—31no—
101C2×#235—61no—
102C3×#131—34no—
103C3×#131—62no—
104C2×C3×M16—31no—
105C2×C3×M16—31no—
106C2×C3×M16—61no—
107C22×C3×C8—31no—
108C22×C3×C8—61no—
109C2×C3×C42—31no—
110#950—34no—
111#950—34no—
112#950—34no—
113#950—34no—
114#950—64no—
115#950—64no—
116#948—22no—
117#948C2×D314yescomplemented
118C2×#216—31no—
119C2×#216—31no—
120C2×#216—61no—
121C2×#215—31no—
122C2×#215—31no—
123C2×#215—61no—
124C2×#214—31no—
125C2×#214—31no—
126C2×#214—61no—
127C2×#213—31no—
128C2×#213—31no—
129C2×#213—61no—
130C2×C4×Dic3C2×D311yescharacteristic
131C2×#208—21no—
132C2×#208C2×D311yescharacteristic
133C2×#208C2×D311yescharacteristic
134C22×C3⋊C8—21no—
135C22×C3⋊C8—31no—
136C22×C3⋊C8—31no—
137C22×C3⋊C8—61no—
138C22×C3⋊C8C2×D311yescharacteristic
139#907—34no—
140#907—62no—
141#901—34no—
142#901—62no—
143C2×ΓL(1,𝔽25)—61no—
144C2×ΓL(1,𝔽25)—61no—
145C2×D3×C8—61no—
146C2×D3×C8—61no—
147C3×#104—34no—
148#837C2×D314yescomplemented
149#825—34no—
150#822—34no—
151#822—34no—
152#815—34no—
153#805—34no—
154#803—34no—
155C23×C32—21no—
156C23×C32#4111yescharacteristic
157C22×C3⋊D3—21no—
158C32×Q8—21no—
159C32×Q8C22×C412yes—
160C32×D4—22no—
161C32×D4—22no—
162C32×D4—21no—
163C32×D4C22×C412yes—
164C2×C32×C4—21no—
165C2×C32×C4—22no—
166C2×C32×C4—22no—
167C2×C32×C4C22×C411yescharacteristic
168C2×C32×C4C22×C411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4#4111yescharacteristic
172C2×C32×C4C2411yescharacteristic
173#638—22no—
174#638—22no—
175C2×C3⋊Dic3—21no—
176C4⋊(C3⋊D3)—21no—
177C4⋊(C3⋊D3)C22×C412yes—
178C4×C3⋊D3—22no—
179C4×C3⋊D3—22no—
180#634—21no—
181#634C22×C412yes—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—42no—
184C3⋊(C3⋊C8)C22×C412yes—
185C3⋊(C3⋊C8)C22×C412yes—
186C3×C3⋊C8—22no—
187C3×C3⋊C8—22no—
188C3×C3⋊C8C2×D412yes—
189C3×C3⋊C8C2×D412yes—
190C2×#135—91no—
191C2×#131—31no—
192C2×#131—91no—
193#444—98no—
194C2×#108—91no—
195C2×#104—31no—
196C2×#104—91no—
197C2×#97—91no—
198C3×#41—21no—
199C3×#41—21no—
200C3×#41—21no—
201C3×#41—21no—
202C3×#41—22no—
203C3×#41—22no—
204C3×#41—41no—
205C3×#41—41no—
206C3×#41C4×D312yes—
207C3×#41C4×D312yes—
208C3×#41C22×D312yes—
209C3×#41C22×D312yes—
210C2×C3×Q8—21no—
211C2×C3×Q8C4×D311yescharacteristic
212C2×C3×Q8C4×D311yescharacteristic
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—41no—
217C2×C3×D4C4×D311yescharacteristic
218C2×C3×D4C4×D311yescharacteristic
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—41no—
223C22×C3×C4—61no—
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C2×#67—61no—
227C2×#67—61no—
228C2×#67—121no—
229C22×Dic3—21no—
230#235—32no—
231#235—32no—
232#235—32no—
233#235—32no—
234#235—62no—
235#235—62no—
236#235—61no—
237#235—61no—
238#235—61no—
239#235—61no—
240#235—121no—
241#235—121no—
242C2×D12—31no—
243C2×D12—31no—
244C2×D12—61no—
245C2×C4×D3—61no—
246C2×C4×D3—61no—
247C2×C4×D3—121no—
248C2×Dic6—31no—
249C2×Dic6—31no—
250C2×Dic6—61no—
251C3×M16—32no—
252C3×M16—32no—
253C3×M16—64no—
254C3×M16—61no—
255C3×M16—61no—
256C2×C3×C8—31no—
257C2×C3×C8—31no—
258C2×C3×C8—32no—
259C2×C3×C8—32no—
260C2×C3×C8—64no—
261C2×C3×C8—61no—
262C2×C3×C8—61no—
263C3×C42—32no—
264C3×C42—61no—
265#216—34no—
266#216—34no—
267#216—64no—
268#215—34no—
269#215—34no—
270#215—64no—
271#214—34no—
272#214—34no—
273#214—64no—
274#213—34no—
275#213—34no—
276#213—64no—
277C4×Dic3—21no—
278C4×Dic3C22×D312yes—
279#208—21no—
280#208—21no—
281#208—24no—
282#208C22×D312yes—
283#208C22×D312yes—
284C2×C3⋊C8—21no—
285C2×C3⋊C8—21no—
286C2×C3⋊C8—24no—
287C2×C3⋊C8—31no—
288C2×C3⋊C8—31no—
289C2×C3⋊C8—31no—
290C2×C3⋊C8—31no—
291C2×C3⋊C8—32no—
292C2×C3⋊C8—32no—
293C2×C3⋊C8—32no—
294C2×C3⋊C8—32no—
295C2×C3⋊C8—61no—
296C2×C3⋊C8—61no—
297C2×C3⋊C8—62no—
298C2×C3⋊C8—62no—
299C2×C3⋊C8#6711yescharacteristic
300C2×C3⋊C8#6711yescharacteristic
301C2×C3⋊C8#6712yes—
302C2×C3⋊C8C22×D312yes—
303ΓL(1,𝔽25)—64no—
304ΓL(1,𝔽25)—64no—
305D3×C8—64no—
306D3×C8—64no—
307C22×C32—22no—
308C22×C32—22no—
309C22×C32—42no—
310C22×C32C4×D411yescharacteristic
311C22×C32C4×D411yescharacteristic
312C22×C32C2×#4111yescharacteristic
313C2×C3⋊D3—22no—
314C2×C3⋊D3—42no—
315C32×C4—22no—
316C32×C4C4×D411yescharacteristic
317C32×C4C4×D411yescharacteristic
318C32×C4C23×C411yescharacteristic
319C32×C4C22×D411yescharacteristic
320C3⋊Dic3—22no—
321C3×Dic3—42no—
322C2×#41—91no—
323C2×#41D3211yescharacteristic
324#135—94no—
325#135—94no—
326C2×Q16—91no—
327C2×SD16—91no—
328C2×SD16—91no—
329C2×D8—91no—
330#131—34no—
331#131—62no—
332#131—94no—
333#131—182no—
334C2×M16—31no—
335C2×M16—31no—
336C2×M16—61no—
337C2×M16—181no—
338C22×C8—31no—
339C22×C8—61no—
340C22×C8—91no—
341C22×C8—181no—
342C2×C42—31no—
343#108—94no—
344#104—34no—
345#104—94no—
346#97—94no—
347C23×C3—21no—
348C23×C3—21no—
349C23×C3—21no—
350C23×C3—41no—
351C23×C3#23511yescharacteristic
352C23×C3#23711yescharacteristic
353C22×D3—61no—
354C22×D3—61no—
355C22×D3—121no—
356C3×Q8—21no—
357C3×Q8—21no—
358C3×Q8—22no—
359C3×Q8—41no—
360C3×Q8C2×C4×D312yes—
361C3×Q8C2×C4×D312yes—
362C3×D4—22no—
363C3×D4—22no—
364C3×D4—22no—
365C3×D4—22no—
366C3×D4—21no—
367C3×D4—21no—
368C3×D4—22no—
369C3×D4—41no—
370C3×D4—42no—
371C3×D4—42no—
372C3×D4C2×C4×D312yes—
373C3×D4C2×C4×D312yes—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—42no—
387C2×C3×C4—42no—
388C2×C3×C4—41no—
389C2×C3×C4—62no—
390C2×C3×C4—122no—
391C2×C3×C4C2×C4×D311yescharacteristic
392C2×C3×C4C2×C4×D311yescharacteristic
393C2×C3×C4C2×C4×D311yescharacteristic
394C2×C3×C4C2×C4×D311yescharacteristic
395C2×C3×C4#23511yescharacteristic
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4#23711yescharacteristic
399C2×C3×C4C2×#6711yescharacteristic
400C2×C3×C4C2×#6711yescharacteristic
401C2×C3×C4C23×D311yescharacteristic
402C2×C3×C4C23×D311yescharacteristic
403#67—62no—
404#67—62no—
405#67—62no—
406#67—62no—
407#67—122no—
408#67—122no—
409C2×Dic3—22no—
410C2×Dic3—42no—
411C2×Dic3—61no—
412C2×Dic3—61no—
413C2×Dic3—121no—
414D12—32no—
415D12—32no—
416D12—62no—
417D12—61no—
418D12—61no—
419D12—121no—
420C4×D3—62no—
421C4×D3—62no—
422C4×D3—62no—
423C4×D3—62no—
424C4×D3—122no—
425C4×D3—122no—
426Dic6—32no—
427Dic6—32no—
428Dic6—62no—
429Dic6—61no—
430Dic6—61no—
431Dic6—121no—
432C3×C8—32no—
433C3×C8—32no—
434C3×C8—62no—
435C3×C8—62no—
436C3⋊C8—22no—
437C3⋊C8—22no—
438C3⋊C8—32no—
439C3⋊C8—32no—
440C3⋊C8—32no—
441C3⋊C8—32no—
442C3⋊C8—62no—
443C3⋊C8—62no—
444C3⋊C8C2×#6712yes—
445C3⋊C8C2×#6712yes—
446C2×C32—21no—
447C2×C32—21no—
448C2×C32—42no—
449C2×C32#44412yescomplemented
450C2×C32C2×C4×D411yescharacteristic
451C3⋊D3—42no—
452#41—21no—
453#41—21no—
454#41—92no—
455#41—92no—
456#41—181no—
457#41—181no—
458#41#62412yes—
459#41C2×D3212yes—
460C2×Q8—91no—
461C2×Q8#62411yescharacteristic
462C2×D4—21no—
463C2×D4—91no—
464C2×D4—181no—
465C2×D4#62411yescharacteristic
466C22×C4—21no—
467C22×C4—61no—
468C22×C4—181no—
469C22×C4C2×D3211yescharacteristic
470Q16—94no—
471SD16—94no—
472SD16—94no—
473D8—94no—
474M16—32no—
475M16—32no—
476M16—64no—
477M16—61no—
478M16—61no—
479M16—184no—
480C2×C8—32no—
481C2×C8—32no—
482C2×C8—31no—
483C2×C8—31no—
484C2×C8—64no—
485C2×C8—61no—
486C2×C8—61no—
487C2×C8—92no—
488C2×C8—91no—
489C2×C8—91no—
490C2×C8—92no—
491C2×C8—184no—
492C42—32no—
493C42—61no—
494C22×C3—22no—
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—42no—
502C22×C3—42no—
503C22×C3—42no—
504C22×C3—42no—
505C22×C3—82no—
506C22×C3#67⋊C411yescharacteristic
507C22×C3#67⋊C411yescharacteristic
508C22×C3C4×#6711yescharacteristic
509C22×C3C4×#6711yescharacteristic
510C22×C3C2×#23511yescharacteristic
511C22×C3C2×#23711yescharacteristic
512C2×D3—62no—
513C2×D3—62no—
514C2×D3—122no—
515C2×D3—122no—
516C2×D3—122no—
517C2×D3—242no—
518C3×C4—22no—
519C3×C4—22no—
520C3×C4—21no—
521C3×C4—21no—
522C3×C4—21no—
523C3×C4—21no—
524C3×C4—42no—
525C3×C4—122no—
526C3×C4#67⋊C411yescharacteristic
527C3×C4#67⋊C411yescharacteristic
528C3×C4C4×#6711yescharacteristic
529C3×C4C4×#6711yescharacteristic
530C3×C4C22×C4×D311yescharacteristic
531C3×C4C22×C4×D311yescharacteristic
532C3×C4C2×D3×D411yescharacteristic
533C3×C4C22×#6711yescharacteristic
534Dic3—42no—
535Dic3—62no—
536Dic3—62no—
537Dic3—122no—
538C32C2×#44411yescharacteristic, complemented, Sylow
539C23—21no—
540C23—181no—
541C23#380411yescharacteristic
542Q8—21no—
543Q8—92no—
544Q8—181no—
545Q8C2×#62412yes—
546D4—22no—
547D4—22no—
548D4—21no—
549D4—92no—
550D4—182no—
551D4—182no—
552D4—181no—
553D4C2×#62412yes—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—62no—
558C2×C4—122no—
559C2×C4—181no—
560C2×C4—182no—
561C2×C4—182no—
562C2×C4#380411yescharacteristic
563C2×C4C2×#62411yescharacteristic
564C2×C4C2×#62411yescharacteristic
565C2×C4D3×#6711yescharacteristic
566C2×C4D3×#6711yescharacteristic
567C2×C4C22×D3211yescharacteristic
568C8—32no—
569C8—32no—
570C8—62no—
571C8—62no—
572C8—92no—
573C8—92no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—22no—
580C2×C3—41no—
581C2×C3—41no—
582C2×C3—42no—
583C2×C3—42no—
584C2×C3—82no—
585C2×C3#482312yescomplemented
586C2×C3#514512yescomplemented
587C2×C3C2×#67⋊C411yescharacteristic
588C2×C3C2×C4×#6711yescharacteristic
589D3—122no—
590D3—122no—
591D3—242no—
592C22—22no—
593C22—22no—
594C22—42no—
595C22—182no—
596C22—362no—
597C22#6395211yescharacteristic
598C22#6395211yescharacteristic
599C22C2×#380411yescharacteristic
600C4—22no—
601C4—122no—
602C4—182no—
603C4#6395211yescharacteristic
604C4#6395211yescharacteristic
605C4C22×#62411yescharacteristic
606C4C2×D3×#6711yescharacteristic
607C3—21no—
608C3C2×#482311yescharacteristic, complemented
609C3C2×#514511yescharacteristic, complemented
610C2—21no—
611C2—21no—
612C2—42no—
613C2—362no—
614C2#1059166312yesdirect product factor
615C2C2×#6395211yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C4×D4
prime radicalC2×#64159C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32C2×#444
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C3×#948C2semidirect
3. C2×#63817C2semidirect
4. C2×C3×#837C2semidirect
5. #10591663C2direct (N × H)
6. C2×#63578C2semidirect
7. C2×#63570C2semidirect
8. C2×#63554C2semidirect
13. #64159C4semidirect
15. C2×#3756C4semidirect
16. C2×#3755C4semidirect
17. C2×#3754C4semidirect
18. C2×#3753C4semidirect
21. C3×#948C22semidirect
30. #63817C22semidirect
32. C3×#837C22semidirect
33. #63578C22semidirect
34. #63570C22semidirect
35. #63554C22semidirect
40. C2×#948D3semidirect
44. C2×#837D3semidirect
71. #3756C2×C4semidirect
72. #3755C2×C4semidirect
73. #3754C2×C4semidirect
74. #3753C2×C4semidirect
117. #948C2×D3semidirect
148. #837C2×D3semidirect
449. C2×C32#444semidirect
538. C32C2×#444semidirect
585. C2×C3#4823semidirect
586. C2×C3#5145semidirect
608. C3C2×#4823semidirect
609. C3C2×#5145semidirect
614. C2#10591663direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#641592
C2×C3×#9482
C2×#638172
C2×C3×#8372
#105916632
C2×#635782
C2×#635702
C2×#635542
C2×#51453
C2×#48233